For some applications, apparatus is provided for facilitating implantation of a prosthetic valve at a native heart valve of a subject, the apparatus comprising a prosthetic valve support, the prosthetic valve support (a) being configured to be transluminally-deliverable to the native valve and to be deployable at the native valve, and (b) comprising one or more tissue-engaging elements, configured to couple the prosthetic valve support to leaflets of the native valve without eliminating check valve functionality of the native valve. Other embodiments are also described.